Employing multi-antenna transmitting and multi-antenna receiving technique in a wireless communication system can improve transmitting capacity of the communication system in many times theoretically. However, at the receiving end in a multi-antenna wireless communication system, signal interference in space domain (i.e., between antennas) exists. When signal transmission is carried out on a single carrier of wide band or multiple carriers of wide sub-bands, the wireless channel of each carrier becomes a frequency selective channel, i.e., inter-symbol interference in different times exists. Therefore, in a frequency selective channel environment, signal interference between different antennas, signal interference in different times, and Additive White Gaussian Noise (AWGN) exist at the receiving end of the multi-antenna system. In a multi-antenna system, the detector part of the receiver must recover the transmitted signals from the multi-antenna receiving signals superposed with signals from different transmitting antennae. The maximum a posteriori probability (MAP) detecting method for interference in time domain and space domain dimensions has unrealizable complexity in case there is a large number of transmitting antennae or multi-paths, and therefore can't be used in practical systems. In ordinary outdoor channel environments, usually direct paths exist, and correlation between antennae exists; for such channels, MMSE or ZF based detecting method can't achieve ideal performance.
In practical communication systems, usually error control encoding is utilized, in order to resist noise and interference; however, high-performance error control encoding methods usually employ soft decision decoding, i.e., the soft information of the bits must be provided, instead of hard decision decoding; therefore, the detector must provide soft information of the bits. At the receiving end, utilizing an iterative detection decoding receiver in which the detector works with the decoder in an iterative mode can greatly improve performance, when compared to a traditional receiver in which the detector and the decoder work with each other in a cascade mode. However, an iterative detection decoding receiver requires that the detector must take soft input and provide soft output, i.e., the detector must can not only soft output decision information to the decoder but also utilize the feedback result from the decoder as a priori information. It is an important task to seek for a soft input and soft output detector that has high performance but low complexity for multi-antenna wireless communication systems in a frequency selective channel environment with spatial correlation and direct path component, in order to support wide application of multi-antenna wireless communication systems.
Suppose the number of transmitting antennae is N, the number of receiving antennae is M, and the number of channel paths is L. In a frequency selective channel, suppose the complex baseband transmitting signal on antenna n in time k is s′n,k, the signal received on receiving antenna m is r′m,k, and set the signal response transmitted from transmitting antenna n to transmitting antenna m in path l is hm,n,l; then the relationship between transmitted baseband signals and received baseband signals is:
                              r                      m            ,            k                    ′                =                                            ∑                              l                =                1                            L                        ⁢                                          ∑                                  n                  =                  1                                N                            ⁢                                                h                                      mn                    ,                    l                                                  ⁢                                  s                                      n                    ,                    k                                    ′                                                              +                      z                          m              ,              k                                                          [        1        ]            
It can be denoted in the following expression in matrix and vector form:
                                          r            k            ′                    =                                                    ∑                                  l                  =                  0                                                  L                  -                  1                                            ⁢                                                H                  l                                ⁢                                  s                                      k                    -                    l                                    ′                                                      +                          z              k                                      ⁢                                  ⁢                              wherein            :                                                  ⁢                          r              k              ′                                =                                    [                                                r                                      1                    ,                    k                                    ′                                ,                                  r                                      2                    ,                    k                                    ′                                ,                …                ⁢                                                                  ,                                  r                                      M                    ,                    k                                    ′                                            ]                        T                          ,                                  ⁢                              s            k            ′                    =                                    [                                                s                                      1                    ,                    k                                    ′                                ,                                  s                                      2                    ,                    k                                    ′                                ,                …                ⁢                                                                  ,                                  s                                      N                    ,                    k                                    ′                                            ]                        T                          ,                                  ⁢                              z            k                    =                                    [                                                z                                      1                    ,                    k                                                  ,                                  z                                      2                    ,                    k                                                  ,                …                ⁢                                                                  ,                                  z                                      M                    ,                    k                                                              ]                        T                          ,                                  ⁢                              H            l                    =                                    [                                                                                          h                                              11                        ,                        l                                                                                                                        h                                              12                        ,                        l                                                                                                  …                                                                              h                                                                        1                          ⁢                          N                                                ,                        l                                                                                                                                                        h                                              21                        ,                        l                                                                                                                        h                                              21                        ,                        l                                                                                                  …                                                                              h                                                                        2                          ⁢                          N                                                ,                        l                                                                                                                                  ⋮                                                        ⋮                                                        ⋱                                                                                                                                                                                                                h                                                                        M                          ⁢                                                                                                          ⁢                          1                                                ,                        l                                                                                                  …                                                                                                                                                                                h                                              MN                        ,                        l                                                                                                        ]                        .                                              [        2        ]            